Monty Hall closes the door

Among much more dramatic news today, I learned about Monty Hall passing away, who achieved long lasting fame among probabilists for his TV game show leading to the Monty Hall problem, a simple conditional probability derivation often leading to arguments because of the loose wording of the conditioning event. By virtue of Stigler’s Law, the Monty Hall game was actually invented earlier, apparently by the French probabilist Joseph Bertrand, in his Calcul des probabilités. The New York Times article linked with the image points out the role of outfits with the game participants, towards being selected by the host, Monty Hall. And that one show had a live elephant behind a door, instead of a goat, elephant which freaked out..!

9 Responses to “Monty Hall closes the door”

1. à propos de Monty Hall,

has a deFinettian view on the problem.

2. […] Hall reminded me of something I was going to write about the Monty Hall Problem, as it did with another blogger I follow, namely that (unsrurprisingly) Stigler’s Law of Eponymy applies to this […]

3. telescoper Says:

As it happens, I have a copy of Bertrand’s book. The problem of ‘trois coffrets’ is Problem 2 of Chapter 1. It is similar to the Monty Hall game, but each box contains two drawers each of which contains a medal. The first box thus contains two gold medals, the second two silver, and the third one gold and one silver.

The game involves choosing a box, then opening one drawer and identifying whether the medal is silver or gold. What is the probability that the medal in the other drawer of the same box is different?

• Thank you for this precision on Bertrand’s coffrets and tiroirs! Is the drawer opened at random or by an operator in the know like Monty?

• Here is the entire quote (pardon my French!):

“Trois coffrets sont d’apparences identiques. Chacun a deux tiroirs, chaque tiroir renferme une médaille. Les médailles du premier coffre sont en or, celles du second en argent, le troisième coffre contient une médaille d’or et une médaille d’argent.
On choisit un coffret ; quelle est la probabilité de trouver dans ses tiroirs une pièce d’or et une pièce d’argent?

Trois cas sont possibles et le sont également puisque les trois coffrets sont d’apparences identiques. Un cas seulement est favorable : la probabilité est 1/3.

Le coffret est choisi. On ouvre un tiroir. Quelle que soit la médaille qu’on y trouve, deux cas seulement restent possibles. Le tiroir qui reste fermé pourra contenir une médaille dont le métal diffère ou non de la première. Sur ces deux cas, un seul est favorable, celui du coffret dont les pièces sont différentes. La probabilité d’avoir mis la main sur ce coffret est donc 1/2.

Comment croire, cependant, qu’il suffise d’ouvrir un tiroir pour changer la probabilité, et de 1/3, l’élever à 1/2 ?”

With the interesting switch from medal (médaille) to coin (pièce), although pièce also means a generic item…

4. Hiroaki Minato Says:

Stigler, not Stiegler… (also in your older post)

• Thank you.

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